Sort through the mussels and discard any that have broken shells. If there are any that have beards, remove the beards. Set aside.

In a large pot, heat olive oil over medium-high heat. Add garlic and shallots. Saute until they soften, about 1 minute. Add sausage slices. Let the pieces sear, turning as needed. Add the white wine. Stir and gently scrape the bottom of the pot to deglaze it. Let the wine reduce until the pot is almost dry. Add the chicken broth and cook until it has reduced by half.

Add lemon juice, butter, salt and pepper to taste, and thyme leaves. Stir to make sure the butter is incorporated into the broth. Raise the heat to high. Add the mussels, cover the pot and steam until all the shells are open, about 5 to 7 minutes.